Another (easier) physics question re gravity

[Alex Franke]

Some of you already know about my issues with gravity (photons, empty spheres, rain barrels, etc), and I appologize in advance for bringing the subject up again. But now that all the physicists are chiming in, I was hoping someone could answer this nagging question I've had.

Say I climb to the top of the leaning tower of Pisa with a ping-pong ball and a bowling ball, and Pisa just happens to be in a vaccuum at the time. I've been taught that if I drop them both at the same time, they'll hit the ground at the same time because the mass isn't supposed to matter.

But what if my bowling ball had a mass of 6x10^23 kg (roughly the mass of the planet, as I recall)? Wouldn't it fall twice as fast? I mean, wouldn't the bowling ball and the Earth come together twice as quickly?

[Ed62]

Well, you suckered me in. I thought it was an easy one.

Ed

[Russianwolf]

No.

The reason is that the mass of your bowling ball would also effect the pingpong ball. So it would pull the ping pong ball along with it at a faster rate. If the bowling ball were to get between the ground and the pingpong ball, then the pingpong ball would speed up as it has twice the gravitational mass of earth pulling at it now. Once it moved in between the bowling ball and earth it would slow as it has a mass behind it pulling it back.

Of course I haven't a clue if I'm right.

And if the bowling ball and the earlth had equal mass, why wouldn't the earth jump up to meet the ball before the ball could fall?

[Uncle Cracker]

I like redeye gravity on my mashed potatity...

[Alex Franke]

Well, you suckered me in. I thought it was an easy one.

Well, at least I thought it seemed like an easy one. All i know for sure is that the tower would lean more.

It's okay if they're dropped at different times (although I have to admit it's interesting to think of what happens when they're dropped at the same time). I guess my thought is this: The mass of the balls does affect how fast they fall -- you'd just never notice it when what you're dropping is much less massive than what you're dropping it on.

[LCHIEN]

i know you couldn't carry that sucker up the tower of pisa,




it doesn't have an elevator, ha.

[Otter]

The real question has to do with how you were holding them, by the top or from the bottom.... the bowling ball has the greater volume would have a head start if you were holding them by the top.

This would effect the timing but not the basics that they woudl accelerate at the same rate.

I find that this guy below has a great way of putting this kind of stuff into easy to read format.

http://www.jimloy.com/physics/galileo.htm

[Mr__Bill]

Ok, lets try this on for size. The object with the mass of earth would still move towards the earth at the same speed as the ping-pong ball. However, the earth would be moving towards the object at the same speed, thus the time to collision would be half the time of the ping-pong ball, as the ball has insufficient mass to attract the earth.
You best experiment with the ping-pong ball first as after the second experiment there may not be much left to the tower, Pisa, Italy and that side of the planet.

Bill, who lives on the other side of the planet.

[MilDoc]

From the above quoted site:

"It would seem that Einstein's General Relativity (a more accurate law of gravity) says that a heavier object actually does accelerate very slightly faster than does a lighter object, in a vacuum."

If that is correct than I vote for the much much heavier mass falling faster.

[LCHIEN]

there's other problems with the problem as posed. An object with that much mass and density equal to the earth would have a diameter of around 6000 miles or so and would be contact with the earth because pisa is only a couple hundred feet high and physics problems are always calculated from the center of mass. Now if the ball were a black hole or even a neutron star then its mass could be as given and be the size of a pea. But then we are talking a whole new set of relativisntic behaviors.

[Tom Slick]

you would have exploded as soon as you stepped into the vacuum in Pisa, never able to drop the objects.

[radhak]

If the bowling ball had the same volume as the earth, it'd be very difficult to take it to the top of the tower. So let's assume it's a regular sized ball (10 inches across) but with the mass of the earth. Again, we have to make some concessions : if the ball was always with that mass, then who's gonna lift it to take it up the tower? Anybody volunteering, should try carrying a PC pancake compressor - which is of slightly less mass - up that height.

So let's make it easier - the mass of the ball can be switched on/off, and for this experiment we switch it on at the last moment, before letting it go from the top. But as soon as it attains the mass of the earth, it's gravity pull will be the same as of the earth, which means "letting it go" would be as tough as throwing the earth to the moon. Trust me - I have tried, and it does not work.
In other words, if the ball in your hand gets the gravity of earth, you are stuck to it. Not only that, the ping-pong ball might not go anywhere either, it's gonna 'fall' to the bowling ball, instead of to the earth. Furthermore, the tower of Pisa might lean more, much more.

After all that reasoning, I give up - I don't wanna volunteer to check Alex's question. I am not into handling two balls of such varying properties as such...

[twistsol]

Hypothetical physics questions are fun because we can throw out facts that we don't want to deal with. In this case, throw out the gravitational pull between the bowling ball and the ping pong ball.

Since the bowling ball and the earth have the same mass, the acceleration would in fact be doubled. However, since they have the same mass, the earth would accelerate up towards the bowling ball as well as the bowling ball accelerating towards the earth.

Therefore from the perspective of the ping pong ball, it would accelerate towards the earth at the normal rate and the earth would accelerate up at the same rate. It would then appear then that the acceleration between the two is double and it would still strike the ground at the same time as the bowling ball.

I suppose you could find a way to tether the earth to a fixed point with one of the massless strings with infinite strength that only physics professors have. Then we'd have a whole different problem.

Generally I prefer road runner physics ... e.g. gravity has no effect until you notice you're not standing on anything and have had a chance to mug for the camera.

[cwithboat]

I would like to point out that this is a three body problem. Unsolvable except in very specialized cases.

[billwmeyer]

I think that the ping pong ball would hit first, because the bowling ball would hit that darn airplane on the conveyer belt slowing the bowling ball slightly before it would "strike" the earth.

Bill